Search results for "Colombeau Algebras"
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Colombeau Algebras and convolutions generated by self-adjoint operators
2017
The role of convolution of functions in the construction of Colombeau algebras of generalized functions is analyzed, with particular referring to the commutative relation with the derivation operator. The possibility to consider the A-convolution, with A an unbounded self-adjoint operator in Hilbert space, is discussed. K
MR3377117 Reviewed Giordano, Paolo; Nigsch, Eduard A. Unifying order structures for Colombeau algebras. Math. Nachr. 288 (2015), no. 11-12, 1286–1302…
2015
Colombeau Algebras are differential algebras of generalized functions (that include the space of distributions) that are defined using a quotient set procedure involving particular classes of nets in a basic space E = (C∞(Ω))A, where Ω is an open subset of R n and A is an index set. The choice of such nets depends mainly on their asymptotic behavior over a suitable index set A. Many variants of Colombeau Algebras existing in the literature occur mainly due to different choices of the index set (and to the choice of asymptotic behavior). A purpose of this paper is to formally unify some of these algebras, redefining the asymptotic behavior on an abstract (pre-ordered) set of indices, and gen…